When to repair engineered floor truss damaged by cut

First off let me quote the American Wood Council PRESCRIPTIVE RESIDENTIAL WOOD DECK CONSTRUCTION GUIDE (which I recommend looking through).

MANUFACTURED WOOD I-JOIST: Many new homes constructed with wood I-joists include 1" or thicker engineered wood products (EWP) – such as oriented strand board (OSB) or structural composite lumber (SCL) including laminated veneer lumber (LVL) – as band joists (or rim boards) that can support the attachment of a deck. However, some older homes might be constructed with band boards that are too thin (less than 1") to support a deck. In such cases, a free-standing deck or a full plan submission is required.

You asked:

Question 1: I assume that if these clips are still being produced that it must be code assuming proper lag screws and spacing have secured the ledger board?

Yes.

It doesn't matter how the joists have bearing, whether it is a hanger, ledger, or beam. Just use the appropriate hardware/fasteners for the application.

Question 2: If I were to cut away the masonry and lag into the 2x6 studs for the ledger support, would this be a sturdy code compliant ledger board?

Back in the "good old days" when homes were balloon-framed they would use let-in ledgers or ribbon boards to support the floor framing (which was also nailed to the studs, though). So, it is doable, but you may need special permission or even engineer's drawings/specs for approval (might also include blocking and extra hardware). Either way, I would say it is not exactly ideal, but at least you could use structural screws like Ledgerloks or GRKs, since they are smaller diameter and self-drilling and not nearly as likely to split the studs.

(balloon-framed, ribbon-board (ledger) and fire-blocking)

And finally, if applicable, if I were to cut away the masonry to mount a ledger board, I would be worried about water possibly penetrating and getting behind the decorative masonry.

You would have the same worries doing the same thing when cutting out siding for a ledger. Flashing to the rescue :)

Question 3: What is the most appropriate way to prevent water from getting behind my ledger board or the masonry?

Again, flashing is the most important part (aside from proper fastening). You have to lap the flashing properly with the building paper. Just remember the direction water flows so the surfaces have to lap the same way a shingle would. See image below for a good illustration of proper flashing. You can also read this short article describing some of the flashing material choices.

After all that, I would say your best bet is to verify your rim board thickness and do a normal ledger. The second best option is a free-standing deck.

Just be careful there is a lot of bad advice and information on the internet!

You really need an engineer to give you an answer and sign off on this. But, being this is the internet, here's my $0.02 anyway.

Your best bet is to replace the whole joist if feasible and not to disruptive to the rest of the structure. But it will be very disruptive to the rest of the structure & flooring and probably impossible to get it into those foundation pockets on both sides. So...

I would cut the existing joist back to the middle of that knee wall or 2x4 nearest the foundation wall. Not counting on that structurally, but you need to square off the end of the existing joist and it makes a convenient place to put the end of the new joist while you tie things together. Take off that little bit of 2x4 back near the drain pipe.

Then I would slide a new piece of joist into the pocket in the foundation wall and flush with the end of the existing joist on top of that 2x4.

Then I would sister the joist on both sides with 2x dimensional lumber of the same height as the existing joist from the foundation wall pocket back to at least 2' to 3' past the end of that huge notch. Be generous with construction adhesive, then clamp the whole thing up and put a few bolts through to pull it together and nail it along the length.